On Cosets of Weight 4 of $BCH(2^{m},8), m$ Even, and Exponential Sums
Pascale Charpin, Tor Helleseth, Victor A. Zinoviev · SIAM Journal on Discrete Mathematics · 2008
We give exact expressions for the number of coset leaders in the cosets of weight 4 of binary primitive narrow sense Bose–Chaudury–Hocquenghem (BCH) codes of length $n=2^m$ (m even) with minimum distance 8 in terms of several exponential sums, including cubic sums and Kloosterman sums. This allows us to bound the number of coset leaders in these cosets.